Finding strong pseudoprimes to several bases
WebMar 24, 2024 · Carmichael numbers are odd composite numbers that are Fermat pseudoprimes to every base; they are sometimes called absolute pseudoprimes. The following table gives the number of Poulet numbers psp(2), Euler-Jacobi pseudoprimes ejpsp(2), and strong pseudoprimes spsp(2) to the base 2, and Carmichael numbers … WebAt last we speed our algorithm for finding larger $C_3$-spsp’s, say up to $10^ {50}$, with a given signature to more prime bases. Comparisons of effectiveness with Arnault’s and our previous methods for finding $C_3$-strong pseudoprimes to the first several prime bases are given. References Similar Articles Additional Information
Finding strong pseudoprimes to several bases
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WebStrong pseudoprimes to twelve prime bases HTML articles powered by AMS MathViewer by Jonathan Sorenson and Jonathan Webster PDF Math. Comp. 86 (2024), 985-1003 Request permission Abstract: Let ψ m be the smallest strong pseudoprime to the first m prime bases. This value is known for 1 ≤ m ≤ 11. We extend this by finding ψ 12 and ψ 13. Webadshelp[at]cfa.harvard.edu The ADS is operated by the Smithsonian Astrophysical Observatory under NASA Cooperative Agreement NNX16AC86A
WebIn this paper we tabulate all strong pseudoprimes (spsp’s) n<1024 to the first ten prime bases 2, 3, ·· · , 29, which have the form n = pq with p, q odd primes and q −1 =k(p −1),k=2, 3, 4. There are in total 44 such numbers, six of which are also spsp(31), and three numbers are spsp’s to both bases 31 and 37. WebApr 1, 2001 · In this paper we tabulate all strong pseudoprimes (spsp’s) n<10 24 to the first ten prime bases 2,3,⋯,29, which have the form n=pq with p,q odd primes and q-1=k (p-1), k=2,3,4· There are in...
WebZhang’s paper shows how to find a much smaller number of composite numbers that might be strong pseudoprimes. He picks numbers k > 1, then picks primes q such that q is larger than the largest prime factor of k, and kq < 10^9. He also cites other papers that show the first strong pseudo prime that isn’t square free must be very large. WebThe Baillie–PSW test is a combination of a strong Fermat probable prime test (that means Miller-Rabin) to base 2 and a strong Lucas probable prime test. The Fermat and Lucas test each have their own list of pseudoprimes, that is, composite numbers that pass the test. For example, the first ten strong pseudoprimes to base 2 are
WebIf you want a bit better results, you could create a sieve of pseudo-primes for the first 20 primes, then you can quickly check which set of 10 gets you furthest, and then you can check larger bases to see which ones will catch the few counterexamples that you have.
WebJan 1, 2002 · Finding strong pseudoprimes to several bases. II October 2003 · Mathematics of Computation Zhenxiang Zhang Min Tang ... [Show full abstract] October 1975 Nigel J. Keen The aperture efficiency of... how to turn on ken haki gpoWebFinding strong pseudoprimes to several bases. Mathematics of computing. Discrete mathematics. Mathematical analysis. Numerical analysis. Number-theoretic … how to turn on keep inventory minehut serversWebShow that the composite number 1281 is a strong pseudoprime base 41. "$n-1=2^rm$, then n is a strong pseudoprime base b if either $b^m=1modn$ or $b^{2^sm}=-1modn$" Ok ... how to turn on keep inventory pcWebMar 24, 2024 · A primality test that provides an efficient probabilistic algorithm for determining if a given number is prime. It is based on the properties of strong pseudoprimes. The algorithm proceeds as follows. Given an odd integer n, let n=2^rs+1 with s odd. Then choose a random integer a with 1<=a<=n-1. If a^s=1 (mod n) or … how to turn on keep inv in minecraft javaWebIn this paper, we first follow the first author’s previous work to use biquadratic residue characters and cubic residue characters as main tools to tabulate all strong … ordway co newspaperWebApr 1, 2001 · Finding strong pseudoprimes to several bases. Author: Zhenxiang Zhang ... how to turn on keep inv minecraftWebtabulate all strong pseudoprimes (spsp's) n < 1024 to the first five or six prime bases, which have the form n p q with p, q odd primes and q - 1 = k(p-1), k = 4/3, 5/2, 3/2, 6; … how to turn on keyboard backlight panasonic